{"id":4877,"date":"2010-10-30T22:46:56","date_gmt":"2010-10-30T21:46:56","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=4877"},"modified":"2022-01-14T23:23:10","modified_gmt":"2022-01-14T23:23:10","slug":"uma-piramide-triangular-regular","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=4877","title":{"rendered":"Uma pir\u00e2mide triangular regular"},"content":{"rendered":"<p><ul id='GTTabs_ul_4877' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_4877' class='GTTabs_curr'><a  id=\"4877_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_4877' ><a  id=\"4877_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_4877'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>O per\u00edmetro da base de uma pir\u00e2mide triangular regular (a base \u00e9 um tri\u00e2ngulo equil\u00e1tero) \u00e9 igual a 24 cm.<\/p>\n<p>O ap\u00f3tema da pir\u00e2mide \u00e9 igual ao dobro da aresta da base e a altura da base mede 6,9 cm.<\/p>\n<p>Determina:<\/p>\n<ol>\n<li>a \u00e1rea de uma das faces laterais;<\/li>\n<li>a \u00e1rea lateral;<\/li>\n<li>a \u00e1rea total.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_4877' onClick='GTTabs_show(1,4877)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_4877'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>\n<div style=\"z-index: 1;\"><span class=\"alignright\"><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"float: right;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":331,\r\n\"height\":398,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"showFullscreenButton\":true,\r\n\"language\":\"pt\",\r\n\/\/ use this instead of ggbBase64 to load a material from GeoGebraTube\r\n\/\/ \"material_id\":12345,\r\n\"ggbBase64\":\"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\"};\r\n\/\/ is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 1,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\n<\/script><\/span>Como a base da pir\u00e2mide \u00e9 um tri\u00e2ngulo equil\u00e1tero, ent\u00e3o o comprimento da aresta da base \u00e9 $a=\\frac{{{P}_{b}}}{3}=\\frac{24}{3}=8\\,cm$.<\/p>\n<p>O comprimento do ap\u00f3tema da pir\u00e2mide \u00e9 ${{a}_{p}}=2\\times 8=16\\,cm$.<\/p>\n<p>Logo, a \u00e1rea de uma face lateral \u00e9 ${{A}_{fL}}=\\frac{a\\times {{a}_{p}}}{2}=\\frac{8\\times 16}{2}=64\\,c{{m}^{2}}$.<br \/>\n\u00ad<\/p>\n<\/div>\n<\/li>\n<li>\n<div style=\"z-index: 1;\">A superf\u00edcie lateral da pir\u00e2mide \u00e9 constitu\u00edda por tr\u00eas tri\u00e2ngulos geometricamente iguais.<\/p>\n<p>Logo \u00e1 \u00e1rea lateral da pir\u00e2mide \u00e9\u00a0${{A}_{L}}=3\\times {{A}_{fL}}=3\\times 64=192\\,c{{m}^{2}}$.<br \/>\n\u00ad<\/p>\n<\/div>\n<\/li>\n<li>\n<div style=\"z-index: 1;\">A \u00e1rea da base da pir\u00e2mide \u00e9 ${{A}_{b}}=\\frac{a\\times c}{2}=\\frac{8\\times 6,9}{2}=27,6\\,c{{m}^{2}}$.<\/p>\n<p>Logo,\u00a0a \u00e1rea total da pir\u00e2mide \u00e9 ${{A}_{T}}={{A}_{b}}+{{A}_{L}}=27,6+192=219,6\\,c{{m}^{2}}$.<\/p>\n<\/div>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_4877' onClick='GTTabs_show(0,4877)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O per\u00edmetro da base de uma pir\u00e2mide triangular regular (a base \u00e9 um tri\u00e2ngulo equil\u00e1tero) \u00e9 igual a 24 cm. O ap\u00f3tema da pir\u00e2mide \u00e9 igual ao dobro da aresta da&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":13768,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,102],"tags":[424,108,67],"series":[],"class_list":["post-4877","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-do-espaco-ao-plano","tag-8-o-ano","tag-area","tag-geometria"],"views":3747,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/PiramideTriangular.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4877","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4877"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4877\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/13768"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4877"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4877"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4877"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=4877"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}